COMEDK2018PhysicsUnits and Dimensions
Dimensional formula for the universal gravitational constant G is
Options
- A[ M ⁻¹ ~L ² ~T ⁻² ]
- B[ M ⁰ ~L ⁰ ~T ⁰ ]
- C[ M ⁻¹ ~L ³ ~T ⁻² ]
- D[ M ⁻¹ ~L ³ ~T ⁻¹ ]
Correct answer
C. [ M ⁻¹ ~L ³ ~T ⁻² ]
Step-by-step solution
According to Newton's law of gravitation, F= G m₁ m₂ r² where, F = gravitational force between two bodies of masses m₁ and m₂ , r= distance between the two masses and G= universal gravitational constant. G= F r² m₁ m₂ . [G]= [F] [r² ] [m₁ ] [m₂ ] = [ MLT ⁻² ] [ L ² ] [ M ][ M ] = [ M ⁻¹ ~L ³ ~T ⁻² ]